A particular amount of gas participates separately in the two process given below:
Process-I:
`P_(1)V_(1) underset("expansion")overset("constant pressure")toP_(1)V_(2) underset("decrease in pressure")overset("constant volume") to P_(2)V_(2)`
Process-II
`P_(1)V_(1) underset("decrease in pressure")overset("constant volume")to P_(2)V_(1) underset("expansion")overset("constant pressure")to P_(2)V_(2)`
For which process, work done |w| is maximum?

Explanation

Process-I: Step-I: `w_(1)=-P_(ex)DeltaV=-P_(1)(V_(2)-V_(1))`
Step-II: `w_(2)=0" "[because" the volumes of the system is constant"]`
Total work, `w=w_(1)+w_(2)=-P_(1)(V_(2)-V_(1))`
So, `|w|=|P_(1)(V_(2)-V_(2))|`
Process-II:Step-I: `w_(1)=0` [`because` the volume of the system is constant]
Step-II: `w_(2)=-P_(ex)DeltaV=-P_(2)(V_(2)-V_(1))`
Total work, `w'=w_(1)+w_(2)=-P_(2)(V_(2)-V_(1))`
So, `|w'|=|P_(2)(V_(2)-V_(1))|` [Since `P_(2) lt P_(1),|w'| lt |w|`].